Theorem fneq1i 5387

Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
fneq1i.1	|- F = G

Assertion

Ref	Expression
fneq1i	|- ( F Fn A <-> G Fn A )

Proof of Theorem fneq1i

Step	Hyp	Ref	Expression
1		fneq1i.1	. 2 |- F = G
2		fneq1 5381	. 2 |- ( F = G -> ( F Fn A <-> G Fn A ) )
3	1, 2	ax-mp 5	1 |- ( F Fn A <-> G Fn A )

Syntax hints:   <-> wb 105   = wceq 1373   Fn wfn 5285

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-in 3180  df-ss 3187  df-sn 3649  df-pr 3650  df-op 3652  df-br 4060  df-opab 4122  df-rel 4700  df-cnv 4701  df-co 4702  df-dm 4703  df-fun 5292  df-fn 5293

This theorem is referenced by:  fnunsn  5402  fnopabg  5419  f1oun  5564  f1oi  5583  f1osn  5585  ovid  6085  tfri1d  6444  frec2uzrand  10587  frec2uzf1od  10588  frecfzennn  10608  xnn0nnen  10619  prdsinvlem  13555  dfrelog  15447  edgstruct  15775  nninfsellemeqinf  16155